Time-Consistent Portfolio Selection for Rank-Dependent Utilities in a Constrained Market

References

• [1] Agarwal RP, O’Regan D (2004) A survey of recent results for initial and boundary value problems singular in the dependent variable. Cañada A, Drábek P, Fonda A, eds. Handbook of Differential Equations: Ordinary Differential Equations, vol. 1 (Elsevier, Amsterdam), 1–68.Google Scholar
• [2] Allais M (1953) Le comportement de l’homme rationnel devant le risque: Critique des postulats et axiomes de l’ecole americaine. Econometrica 21(4):503–546.Crossref, Google Scholar
• [3] Basak S, Chabakauri G (2010) Dynamic mean-variance asset allocation. Rev. Financial Stud. 23(8):2970–3016.Crossref, Google Scholar
• [4] Björk T, Khapko M, Murgoci A (2017) On time-inconsistent stochastic control in continuous time. Finance Stochastics 21:331–360.Crossref, Google Scholar
• [5] Björk T, Murgoci A, Zhou XY (2014) Mean–variance portfolio optimization with state-dependent risk aversion. Math. Finance 24(1):1–24.Crossref, Google Scholar
• [6] Calamai PH, Moré JJ (1987) Projected gradient methods for linearly constrained problems. Math. Programming 39(1):93–116.Crossref, Google Scholar
• [7] Carlier G, Dana RA (2006) Law invariant concave utility functions and optimization problems with monotonicity and comonotonicity constraints. Statist. Decisions 24(1):127–152.Google Scholar
• [8] Carlier G, Dana RA (2011) Optimal demand for contingent claims when agents have law invariant utilities. Math. Finance 21(2):169–201.Crossref, Google Scholar
• [9] Cvitanić J, Karatzas I (1992) Convex duality in constrained portfolio optimization. Ann. Appl. Probab. 2(4):767–818.Crossref, Google Scholar
• [10] Ekeland I, Lazrak A (2006) Being serious about non-commitment: Subgame perfect equilibrium in continuous time. Preprint, submitted April 12, https://arxiv.org/abs/math/0604264.Google Scholar
• [11] Ekeland I, Lazrak A (2010) The golden rule when preferences are time inconsistent. Math. Financial Econom. 4(1):29–55.Crossref, Google Scholar
• [12] Ekeland I, Pirvu TA (2008) Investment and consumption without commitment. Math. Financial Econom. 2(1):57–86.Crossref, Google Scholar
• [13] Föllmer H, Schied A (2016) Stochastic Finance: An Introduction in Discrete Time, 4th ed. (De Gruyter, Berlin).Crossref, Google Scholar
• [14] He XD, Jiang ZL (2021) On the equilibrium strategies for time-inconsistent problems in continuous time. SIAM J. Control Optim. 59(5):3860–3886.Crossref, Google Scholar
• [15] He XD, Strub MS, Zariphopoulou T (2021) Forward rank-dependent performance criteria: Time-consistent investment under probability distortion. Math. Finance 31(2):683–721.Crossref, Google Scholar
• [16] Hu Y, Jin H, Zhou XY (2012) Time-inconsistent stochastic linear-quadratic control. SIAM J. Control Optim. 50(3):1548–1572.Crossref, Google Scholar
• [17] Hu Y, Jin H, Zhou XY (2017) Time-inconsistent stochastic linear–quadratic control: Characterization and uniqueness of equilibrium. SIAM J. Control Optim. 55(2):1261–1279.Crossref, Google Scholar
• [18] Hu Y, Jin H, Zhou XY (2021) Consistent investment of sophisticated rank-dependent utility agents in continuous time. Math. Finance 31(3):1056–1095.Crossref, Google Scholar
• [19] Huang YJ, Wang Z (2021) Optimal equilibria for multidimensional time-inconsistent stopping problems. SIAM J. Control Optim. 59(2):1705–1729.Crossref, Google Scholar
• [20] Huang YJ, Zhou Z (2019) The optimal equilibrium for time-inconsistent stopping problems—The discrete-time case. SIAM J. Control Optim. 57(1):590–609.Crossref, Google Scholar
• [21] Huang YJ, Zhou Z (2020) Optimal equilibria for time-inconsistent stopping problems in continuous time. Math. Finance 30(3):1103–1134.Crossref, Google Scholar
• [22] Jin H, Zhou XY (2008) Behavioral portfolio selection in continuous time. Math. Finance 18(3):385–426.Crossref, Google Scholar
• [23] Karatzas I, Lehoczky JP, Shreve SE, Xu GL (1991) Martingale and duality methods for utility maximization in an incomplete market. SIAM J. Control Optim. 29(3):702–730.Crossref, Google Scholar
• [24] Liang Z, Wang S, Xia J (2025) An integral equation in portfolio selection with time-inconsistent preferences. SIAM J. Financial Math. 16(1):SC12–SC23.Crossref, Google Scholar
• [25] Merton RC (1971) Optimum consumption and portfolio rules in a continuous-time model. J. Econom. Theory 3(4):373–413.Crossref, Google Scholar
• [26] Quiggin J (1982) A theory of anticipated utility. J. Econom. Behav. Organ. 3(4):323–343.Crossref, Google Scholar
• [27] Strotz R (1955) Myopia and inconsistency in dynamic utility maximization. Rev. Econom. Stud. 23(3):165–180.Crossref, Google Scholar
• [28] Tversky A, Fox CR (1995) Weighing risk and uncertainty. Psych. Rev. 102(2):269–283.Crossref, Google Scholar
• [29] Tversky A, Kahneman D (1992) Advances in prospect theory: Cumulative representation of uncertainty. J. Risk Uncertainty 5(4):297–323.Crossref, Google Scholar
• [30] Wang SS (2000) A class of distortion operators for pricing financial and insurance risks. J. Risk Insurance 67(1):15–36.Crossref, Google Scholar
• [31] Wei J, Wang T (2017) Time-consistent mean-variance asset-liability management with random coefficients. Insurance Math. Econom. 77:84–96.Crossref, Google Scholar
• [32] Xia J, Zhou XY (2016) Arrow-Debreu equilibria for rank-dependent utilities. Math. Finance 26(3):558–588.Crossref, Google Scholar
• [33] Xu ZQ (2016) A note on the quantile formulation. Math. Finance 26(3):589–601.Crossref, Google Scholar
• [34] Yaari ME (1987) The dual theory of choice under risk. Econometrica 55(1):95–115.Crossref, Google Scholar
• [35] Yong J (2012) Time-inconsistent optimal control problems and the equilibrium HJB equation. Math. Control Related Fields 2(3):271–329.Crossref, Google Scholar
• [36] Yong J (2017) Linear-quadratic optimal control problems for mean-field stochastic differential equations—Time-consistent solutions. Trans. Amer. Math. Soc. 369(8):5467–5523.Crossref, Google Scholar